A lacunary version of Mergelian's approximation theorem

作者：Gharibyan T; Luh W^*; Mueller J

来源：Journal of Approximation Theory, 2010, 162(4): 709-716.

DOI：10.1016/j.jat.2009.09.002

• Mergelian's theorem
• Lacunary approximation

Let K be a compact plane set having connected complement. Then Mergelian's theorem states that the linear span of the monomials z(n), i.e. the polynomials, are dense in the Banach space A(K) of all functions continuous on K and holomorphic in the interior of K endowed with the sup-norm. We consider the question under which conditions the linear span of z(n), with n running through a sequence of nonnegative integers having upper density one, is dense in A (K) or appropriate subspaces.

• 出版日期2010-4